MEPX
Chapter 7 of 11All chapters
  1. 1What probability means
  2. 2Counting outcomes
  3. 3Independent events
  4. 4Dependent events
  5. 5Complements and at least one
  6. 6Adding probabilities
  7. 7Permutations and combinations
  8. 8Conditional probability
  9. 9Expected value
  10. 10Distributions in outline
  11. 11Fallacies and traps

Chapter 7 of 11

Permutations and combinations

Counting when order does or does not matter.

Order matters

Arranging 5 books on a shelf gives 5 factorial, which is 120 orders. Choosing 3 of them for specific positions gives 5 times 4 times 3, which is 60.

  • Factorial counts full arrangements of a set.
  • Multiply the choices at each step and the pattern appears on its own.

Order does not matter

Choosing 3 books to take on holiday is a combination: the same 60 arrangements, divided by the 6 orders of any 3 books, giving 10. Lottery odds are exactly this calculation.